PAGE STATUS: After eight years of study, I have only recently realized this subject is worthy of an entire page because it is at the very heart of all esoteric symbolism. As a result of this narrowing of the focus, I can now begin to expand this page.
LAST UPDATE: September 17, 2021
An introduction to the grandeur of phi and the Fibonacci sequence
The image to the left is often used to represent the 47th Proposition of Euclid, which is just a fancy (and I would add pretentious) way of saying the Pythagorean theorem a2 + b2 = c2 we all learned in high school when calculating the area of a right triangle. In this case, that would be 32 + 42 = 52 or 25. So there are 25 squares in the block that corresponds to the the hypotenuse (the side opposite the right angle). From this simple mathematical formula we derive the term Pythagorean Triple, where sides a and b are whole numbers (or positive integers) such as 3 and 4. 3-4-5 is the smallest Pythagorean triple and is often used in Freemason literature. In fact, a similar image is used in an article entitled The 47th Proposition of Euclid, written by Lodge No. 43 in Lancaster, Pennsylvania in which they explain how to properly measure the Great Pyramid of Giza. This article quotes from Anderson’s Constitutions of 1723 (an important document for the Freemasons) when describing the Pythagoean theorem as “the Foundation of all Masonry, sacred, civil, and military…” But there is more than meets the eye in this representation of the Pythagorean theorem, which is why I think the Freemasons like to use it so much. While focusing on what an artist would call the “positive space” (the white squares), one can easily overlook the black squares. Count them. What you do not see without closer examination is the 5-8-13 Fibonacci sequence defined by the black squares. The relationship between phi and the Fibonacci sequence is at the very core of understanding what I characterize as the “religion” of the progeny of Jove.
“The Great Pyramid, that monument to spirituality that the Agashan Teachers hold in such high esteem, is built according to the principles of Pi and Phi.”
Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.
Like God, the Divine Proportion is always similar to itself.
Wikipedia, Fra Luca Pacioli
It is impossible to explain honestly the beauties of the laws of nature in a way that people can feel, without their having some deep understanding of mathematics. I am sorry, but this seems to be the case.
Wikipedia, Richard Feynman
In a way, the Phi Triangle of the Golden Mean could be compared to the path of light sent forth from the great All-Seeing Eye of God in the beginning, and which paved the way for the creation of the Universe.
William Eisen, The English Cabalah Volume 2, The Mysteries of Phi
Phi is so deeply interwoven into the fabric of the universe that Renaissance artists referred to it as the
And this is the key to understanding Phi. It is not the product of the human mind. It is not of this world. It is…
It is intelligence shared by ET. It is therefore for us an invitation into the galactic community, which is why it is at the heart of all esoteric symbolism as discussed on pages such as № 76. Approximating Phi using the Fibonacci sequence as aspect ratios and № 74. Skull and Bones 322 and corporate logos. You see these people really are not evil. They just disrespect your religion so much that they don’t really care what you think.
Tawdry pretense and feigned, wannabe thuggery
To the rich and powerful European Illuminati who walk among us now, who profess to be the legitimate heirs of all that Pythagoras knew, who control both the government and military of the United States of America as well as the international banking system and all of the major corporations in the so-called “private” sector, and who own mass media lock, stock, and barrel, I say you have inherited the riches of a system of thought you do not truly understand.
For someone who has genuinely felt the awe and wonder of the Golden Ratio, Fibonacci Sequence, and Golden Spiral, pictures such as this one of Madonna flashing 666 is the height of banality. The use of 666 in popular culture has degenerated to the point of being nothing more than a tawdry pretense of knowing or else a meaningless suggestion of thuggishness. The numbers are not inherently evil. As William Shakespeare so famously said, there is nothing either good or bad, but thinking makes it so. So I am just going to quote from the Bible before continuing.
Give not that which is holy unto the dogs, neither cast ye your pearls before swine, lest they trample them under their feet, and turn again and rend you.
Put off thy shoes from thy feet: for the place where thou standest is holy ground
When considered along with pages № 76. Approximating Phi using the Fibonacci Sequence as Aspect Ratios and № 74. Skull and Bones 322 and Corporate Logos, I am about to hand you the keys to all esoteric symbolism. In the Introduction to “The Lost Keys of Freemasonry or The Secret of Hiram Abiff,” Manly P. Hall equates Freemasonry to religion. Here it must be said that he did not join the Freemasons until June 28, 1954, well after the progeny of Jove morphed from the Freemasons to the CIA in 1947. Consequently, there was never an opportunity for him to learn about their specific knowledge of the end time. He is a great man. His works are irreplaceable, but the constant suggestion of unfathomable depths and the mystic he cultivated, even by his very looks, approaches what can only be described as a personality cult. This is the tendency of such people, none so more so than H.P. Blavatsky, co-founder of the Theosophical Society, and her “Demon est Deus inversus” nonsense.
These people are promoting themselves.
The difference between them and the progeny of Jove is significant. The progeny of Jove are about survival. Once you have the keys, their esoteric symbolism is simple to understand and straightforward.
You must not make the mistake of confusing the phony mysticism with the simplicity of the esoteric symbolism discussed on this website.
As stated on my home page, “The progeny of Jove has always counted on the pretentious, pompous, and self-aggrandizing character of most men, what I like to think of as their sophistry, to hide the simplicity of their symbolism. Nothing exhibits this more than the G that was introduced into Freemasonry symbolism upon their arrival on the shores of North America. It means granite. It has always meant granite and is a reference to the Pikes Peak batholith.” I make this point over and over again on this website usually in reference to the G in Freemason symbolism, but the same simplicity can be seen in all of the corporate logos discussed on page № 74. Skull and Bones 322 and Corporate Logos and in the design of the new One World Trade Center discussed on page № 7. The real Horror of the September 11, 2001 (9/11) domestic Terrorist Attack is the Truth.
Through the years the progeny of Jove have relied on what is best described as sophistry to mislead and beguile the pretentious nature of “educated” men who joined their ranks as “novices” in the hope of discovering the profound secret the progeny of Jove are sworn to keep on pain of death. Thus on scottishritenmj.org, we read, “The square and compasses are architect’s tools, and many say that the commonly seen G in the middle represents geometry.” This is utter nonsense.
The answer to this question is simple. In fact, simplicity is the key to unlocking the meaning of symbols used by secret societies such as the Freemasons and Skull and Bone. All the talk about God, the Great Architect, and Geometry is so much mindless prattle. The meaning of the Freemason square and compass is not deep. It is staring you in the face.
The progeny of Jove relay on the sophistry and pretentious nature of “educated” men to belie and obfuscate the simplicity of their symbols.
In that sense, manly P. Hall did us all a great disservice. The “G” stands for granite and is a reference to the Pikes Peak granite batholith in the Front Range, what Virgil called the “vault profound” where the progeny of Jove think they will survive the coming destruction of the planet.
I repeat this message because it is important for you to understand. Simplicity is the key.
The mathematics of the Fibonacci Sequence and Phi
This knowledge is most certainly not the exclusive domain of the mathematically elite. As I am fond of saying, there is always an eloquent simplicity to truth. The concepts of Phi, the Fibonacci sequence, and how they combine in the Golden Spiral are quite easy to grasp. They not only can, but should be taught to your children while they are still quite young. I would argue not later than five years old.
Phi is most often expressed as the decimal fraction1.618 (which is rounded). But Phi is actually an irrational number which means the fractional part of the decimal number cannot be computed because it never ends and never repeats. So unless you use the Greek letter phi (uppercase Φ or lowercase φ) or round to something like 1.618, you could spend eternity writing out Phi as a decimal fraction.
There are many other names (listed in Wikipedia and elsewhere) for the Golden Ratio. They include golden mean or golden section (Latin sectio aurea), extreme and mean ratio (used in one of the quotes at the top of the page), medial section, divine proportion (Latin proportio divina), divine section (Latin sectio divina), golden proportion, golden cut, and golden number. I have started capitalizing Golden Ratio, Fibonacci Sequence, and Golden Spiral out of respect for what they represent. Please note that this is unusual. Normally, only Fibonacci is capitalized.
This image is from Wikipedia, Golden Ratio and is labeled, “Line segments in the golden ratio.”
There is a somewhat complex equation behind arriving at the exact number for Phi, but you do not need to know anything about it. You just need to know the most convenient and commonly used decimal fraction to represent Phi or use it in designing your own work, which is 1.618. For example, I used the Golden Ratio for the first time in designing my “Please help” donation button at the top of each page. It is an example of a golden rectangle.
All of this sounds deceptively simple and, from from a mathematical perspective, it is simple. So why is Phi so important to the progeny of Jove? Because numbers are their religion and always have been since the time of Pythagoras and Phi is one of the two most important sacred numbers. I think you will understand why after reading the next section. The other is 216. As you will see on page № 76. Approximating Phi using the Fibonacci Sequence as Aspect Ratios, the combination of these two sacred numbers is one of only two possible explanations as to why circles have 360 degrees.
Phi and the Fibonacci Sequence are closely related subjects. The Fibonacci Sequence is truly child’s play. Here are the first eleven numbers in the sequence.
As you can see, the next number in the sequence is the sum of the previous two numbers. That’s it. It’s that simple. The magic is in the ratio of two adjacent numbers in the Fibonacci sequence. For the uninitiated, this livescience.com excerpt emphasizes the critical point.
Around 1200, mathematician Leonardo Fibonacci discovered the unique properties of the Fibonacci sequence. This sequence ties directly into the Golden ratio because if you take any two successive Fibonacci numbers, their ratio is very close to the Golden ratio. As the numbers get higher, the ratio becomes even closer to 1.618. For example, the ratio of 3 to 5 is 1.666. But the ratio of 13 to 21 is 1.625. Getting even higher, the ratio of 144 to 233 is 1.618. These numbers are all successive numbers in the Fibonacci sequence. —”What is the Golden Ratio?” by Elaine J. Hom from which I borrowed the image at the Golden Spiral used on this website.
The following table demonstrates this using just enough of the Fibonacci Sequence to arrive at 1.6180 (the emphasis on the last zero). Interestingly, it is the thirteenth row and involves sacred number 144.
The fourth and sixth rows are highlighted because they become very important on page № 76. Approximating Phi using the Fibonacci Sequence as Aspect Ratios.
That is about all you need on the mathematics of Phi and the Fibonacci sequence to understand everything I say about esoteric symbolism on this website. So perhaps now you understand why I felt compelled to begin this page with warnings about phony mysticism. I continue this discussion about the relationship between Phi and the Fibonacci Sequence in the next section.
The Golden Spiral: Phi in nature
Phi is expressed in nature as the Golden Spiral which is based on the Fibonacci sequence and is therefore sometimes referred to as the Fibonacci Spiral. The trick to understanding what is happening here is to realize the Fibonacci sequence is a mathematical expression of how nature produces Phi in the growth of everything from plants to galaxies. Thus both the Golden Ratio and the Fibonacci sequence are discoveries of something found in nature, not the product of human invention. In the Golden Spiral, both the Golden Ratio and the Fibonacci sequence combine as one.
The Golden Spiral
Examples of the Golden Spiral in nature are ubiquitous
But this is my favorite (I will add others)
From a rose to the Milky Way. Phi is Life. Phi is God expressed in numbers.
Phi in geometry
All images are credit Wikipedia unless otherwise noted.
The Golden rectangle is a basic building block in architecture.
As seen above in the images of the Great Pyramid of Giza and Mona Lisa, overlaying the Golden Spiral (sometimes referred to as the Fibonacci Spiral) is a very common way of showing a form incorporates Phi into its design. In this case, the match is perfect because this is a Golden Triangle.
The pentagram includes five golden triangles, which should help to explain the natural fascination with this form (as well as the Pentagon).
Phi in architecture
The quintessential example of Phi in architecture is the Parthenon, which exudes Phi.